An Iraqi pleaded for his life to Donald Trump, a Syrian-born New Yorker wondered how he would get home and church groups stared in dismay at homes prepared for refugee families who may never arrive.

Despair and confusion set in among citizens of seven predominantly Muslim countries who suddenly found themselves unable to enter the United States a day after President Trump signed an order he said was necessary to stop "radical Islamic terrorists" from coming to America.

Included is a 90-day ban on travel to the US by citizens of Iraq, Syria, Iran, Sudan, Libya, Somalia or Yemen and a 120-day suspension of the US refugee programme.

Travellers from those nations were either barred from getting on their flights or detained at US airports after they landed, including tourists, foreign students and people trying to visit friends and family.

"What's next? What's going to happen next?" said Mohammed al Rawi, an Iraqi-born American citizen, after his 69-year-old father, coming to visit his grandchildren in California, was detained and sent back to Iraq after 12 hours in custody.

"Are they going to create camps for Muslims and put us in it?"

After an appeal from civil liberties lawyers, a federal judge in New York issued an emergency order barring the US from summarily deporting people who had arrived with valid visas or an approved refugee application, but the ruling affected only a portion of Mr Trump's order.

Protests broke out at several US airports where travellers were being held, including a gathering of several hundred people outside San Francisco's main airport and a raucous demonstration of at least 2,000 people at New York's Kennedy International Airport.

Hameed Khalid Darweesh, a translator and assistant for the US military in Iraq for 10 years, now fleeing death threats, was among at least a dozen people detained at Kennedy on Friday and Saturday.

He was released after his lawyers and two members of the US Congress went to the airport to try to gain his release.

"This is the soul of America," Mr Darweesh told demonstrators and reporters, adding that the US was home to "the greatest people in the world".

Others were less lucky - Parisa Fasihianifard, 24, arrived after a long trip from Tehran, in Iran, only to be detained and told she had to go home.

"She was crying and she told me she was banned to come inside and go through the gates," said her husband Mohamad Zandian , 26, an Iranian doctoral student at Ohio State University.

Staff at US agencies that resettle refugees, several in tears, were scrambling to analyse the order and prepared for the wrenching phone calls that would have to be made to thousands just days away from travelling to the US.

Meathaq Alaunaibi, a refugee from Iraq, was hoping to soon be reunited with her twin 18-year-old daughters who are in Baghdad and was "crying all the time".

She, her husband, a son and another daughter were settled in Tennessee last August, as the twins completed their government review to enter the US.

"They (her daughters) are so worried and afraid because they're stuck there in Baghdad," she said.

An Iraqi in Mosul, where the Islamic State terror group had seized control, despaired at word that what he had thought was an imminent flight to safety in America was now cancelled indefinitely.

"If you can write to Mr Trump or find any other way to help me reunite with my family, please, I am dying in Iraq, please," the man, whose identity was withheld because he is still in danger in Iraq, wrote back to his US lawyer by email.

The order also caused confusion for longtime, legal US residents travelling abroad.

Kinan Azmeh, a clarinetist born in Syria who has lived in the US for 16 years, left his home in New York City three weeks ago for a series of concerts that included a date with cellist Yo-Yo Ma, but does not know if he will be able to return.

"It (New York City) is home as much as Damascus", he said by phone from Lebanon.

Before Mr Trump signed the order, more than 67,000 refugees had been approved by the government to enter the US, said Jen Smyers, refugee policy director for Church World Service.

More than 6,400 had already been booked on flights, including 15 families that had been expected over the next few weeks in the Chicago area from Ethiopia, Eritrea, Iran, Syria and Uganda.

Most refugees entering the US are settled by religious groups which liaise with churches, synagogues and mosques to collect furniture, clothes and toys for the refugees and set up volunteer schedules for hosting duties.

In Massachusetts, Jewish Family Service of MetroWest had been co-ordinating a group of doctors, community leaders, a local mosque and other volunteers to resettle 15 Syrian families.

Now, two fully-outfitted apartments remain empty and it is unclear when, if ever, the other refugees will be allowed to enter, said Marc Jacobs, the group's chief executive.

Nour Ulayyet of Valparaiso, Indiana, said her sister, a Syrian living in Saudi Arabia, was sent back after arriving from Riyadh at Chicago's O'Hare International Airport on Saturday and told she could not enter the US to help care for their sick mother.

Ms Ulayyet said some airport officials were apologising to her sister, who had a valid visa.